Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Entropy production and the rate of convergence to equilibrium for the Fokker-Planck equation


Author: G. Toscani
Journal: Quart. Appl. Math. 57 (1999), 521-541
MSC: Primary 82C31; Secondary 35Q99
DOI: https://doi.org/10.1090/qam/1704435
MathSciNet review: MR1704435
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Abstract: We reckon the rate of exponential convergence to equilibrium both in relative entropy and in relative Fisher information, for the solution to the spatially homogeneous Fokker-Planck equation. The result follows by lower bounds of the entropy production which are explicitly computable. Second, we show that the Gross's logarithmic Sobolev inequality is a direct consequence of the lower bound for the entropy production relative to Fisher information. The entropy production arguments are finally applied to reckon the rate of convergence of the solution to the heat equation towards the fundamental one in various norms.


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DOI: https://doi.org/10.1090/qam/1704435
Article copyright: © Copyright 1999 American Mathematical Society


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